Phase-Field Modeling and Simulations of Lipid Membranes Coupling Composition with Membrane Mechanical Properties

Abstract

The plasma membrane, a lipid bilayer membrane surrounding all mammalian cells, is not homogeneous, but rather contains domains termed ‘rafts,’ defined as regions enriched with cholesterol and saturated lipids. Understanding how and why these rafts form is of great importance to cell biologists and immunologists, since they are involved in many important cell functions and processes including endocytosis, cell adhesion, signaling, protein organization, lipid regulation, and infection by pathogens. These raft structures also show great potential for technological applications, especially in connection with biosensors and drug delivery systems. We examine the formation and evolution of lipid raft-like domains in multicomponent lipid membrane vesicles using a continuum-level simulation method. Our objective is to investigate how various physical parameters input into the model, such as spontaneous curvature, bending rigidity, and phase fraction, affect the dynamics and equilibrium morphological phases formed in two-phase lipid membrane systems. This model is applied to membranes with spherical background geometries, simulating the compositional and shape evolution of lipid vesicles, coupled using a modified Helfrich free energy. The compositional evolution is modeled using a phase-field method and is described by a Cahn-Hilliard-type equation, while the shape changes are described by relaxation dynamics in which the vesicle surface area is conserved. We find that the compositional and morphological evolution are significantly altered when the mechanical coupling is present by comparing the results with those of systems where this coupling is absent. More specifically, we find that the evolution is significantly slowed when the phases have equal and opposite spontaneous curvatures and are present in roughly equal amounts. We also investigate equilibrium shapes formed by completely phase-separated vesicles as a function of spontaneous curvature, bending rigidity, and phase fraction.